The married country singer released a public apology to his wife last week, when TMZ released photographs of Aldean and Kerr embracing at an LA bar.
"The truth is that I screwed up. I had too much to drink, let the party get out of hand and acted inappropriately at a bar," Aldean wrote in an open letter. "I left alone, caught the bus to our next show and that's the end of the story."
Aldean has now admitted in an interview with CMT Insider that the incident caused a strain on his marriage to high school sweetheart Jessica Ussery.
"I think when it comes to all the things that have been going on lately, I mean, it's just been a tough situation," the 'Fly Over States' star said.
He continued: "I know everybody's kinda going to have their opinion, and for the people that know me and know what I'm about... the people that are standing by us and supporting us, all I've got to say to them is thanks.
"I mean, I really appreciate it, and it's just been a really unfortunate thing. Really embarrassing, I think, more than anything."
[Jason Aldean pictured above with wife Jessica Ussery at 2012 CMT Awards]
Aldean went on to insist that his marriage will survive the embarrassment he has caused.
"The main thing is that me and my family are okay, and everything's good there," he assured his fans. "I think it's been a tough deal.
"But I kind of said what I needed to say to them and, hopefully, they understand that. And the rest of it will be us dealing with it in private and trying to fix it."
American Idol's Kerr has also publicly expressed regret for causing any pain to Aldean's family.
Kerr wrote in a press statement: "The actions I portrayed recently were not a representation of my true character, but a lapse in judgment on my part.
"I would like to sincerely apologise to everyone that has been affected by this, including my friends & family."
Aldean is to kick off a limited number of live dates later this month. He will next perform in San Antonio, TX on October 25.
New! Digital Spy breakfast show - watch Amie Parker-Williams discuss the day's biggest stories including Girls Aloud, The X Factor's Carolynne and more: